Does Batman Equation really work? And can we "union" relations? (Sorry for long reply.)

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Does Batman Equation really work? And can we "union" relations? (Sorry for long reply.)

Mathematics
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I just happened to discover this question in Math Stack Exchange (MSE): http://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real/54568#54568 Here's the image: |dw:1435886055793:dw| http://i.stack.imgur.com/VYKfg.jpg I tried to graph it on Desmos: https://www.desmos.com/calculator/cscx2zcrlf Graphing each factor separately turns out well, however when I multiply all factors, graph won't appear. I think Desmos just choke on it, so I tried something simple; https://www.desmos.com/calculator/enxuzekis6 Yet it doesn't show anything... So apparently image above is not true. My questions are: \(\Large 1)\) Is there any way to union relations? By "union," I mean in \(\mathbb R^2\), if you union \(f(x,y)=0\) and \(g(x,y)=0\), then you would have new union relation \(U(x,y)=0\), which if you graph it, then \(f(x,y)=0\) and \(g(x,y)=0\) would both be graphed simultaneously. From image, it's \(U(x,y) = f(x,y)g(x,y)=0\), but it seems that it is not true. \(\Large 2)\) Why does no one seem to notice that image is not true in MSE question?
A relation is a set, so obviously you could union two relations.
Yeah I know. Not sure what's correct word for that, but let's just stick with "union" By "union," I mean saying if you graph \(f(x,y)=0\) and \(g(x,y)=0\), you would see something on xy plane. If we "union" these relations, then we would have new relation \(U(x,y)=0\), such that if you graph \(U(x,y)\), then you would see same thing as if you graph \(f(x,y)=0\) and \(g(x,y)=0\) separately at the same time.

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From shown image, you just multiply relations, but to me, it doesn't work.
In my opinion it doesn't work :/ very complex and in testing ur not going to really make a perfect batman sign on the graph xD
We are such math nerds XD
For example; saying we have \(f(x,y) = x^2+y^2 -1= 0\) and \(g(x,y) = (x+2)^2+y^2-1=0\) Then \(U(x,y)\) would graph this:|dw:1435887037303:dw| Exactly what is \(U(x,y)\)? and how can I "combine" f(x,y) and g(x,y) to form U(x,y)?
Wut now it works. https://www.desmos.com/calculator/uezz1quzdy Now I am confused lol...
Got something to do with restrictions, I guess. That circles equation above here has no restriction, but Batman Equation does.
https://www.desmos.com/calculator/enxuzekis6 First relation is restricted to \(x>1\) Second relation is restricted to \(x<1\) So together they would not appear in graph simply because they would be somewhere in complex. Just like Batman Equation. Is there any way to prevent that? OK I think that's too much to ask lol...
@iambatman ( ͡° ͜ʖ ͡°)
Im batman (in husky batman voice) o.o
Yes, the roots of \(f\cdot g\) is the union of the roots of \(g\) and the roots of \(f\).
Only exceptions are when you have different domains
You intersect the domains, then you union the roots in that intersected domain
OK, I think I asked rather silly and pointless question. But thanks for put in effort for me.
Superman > Batman
nincompoop I am afraid you made a mistake, it should be: Superman < Batman
That's super cool. I wonder if there will be a bunch of equations that can produce the Avengers Logo? When I was taking Calculus III there were some equations in polar coordinates that produced flowers, the number 8, or the infinity symbol.
Anyway, graphing these equations separately was a good idea. If it was bunched up together, wouldn't something overlap and eventually the Batman Logo will no longer appear?
@iambatman should know xD
Haha, I believe it was here I posted something similar long time ago, in any case it seems you've figured out what your problem was? @geerky42 @nincompoop I resent that!
FYI - Here is the Batman Equation implemented in Geogebra: \( \href{http:///www.geogebra.org/m/114}{Batman}\)

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